Children's drinking cups are generally provided with removable lids, to help prevent large spills. Commonly, these lids have drinking spouts extending from their upper surface, that children place in their mouths to sip from the cups. Such cups are sometimes called “sippy cups.” Some sippy cup spouts have open slots or holes through which the liquid in the cup flows when the cup is inverted. Such slots or holes are generally sized for an acceptably high flow rate, for ease of cleaning, and to enable the passage of small drink particulates such as pulp in orange juice. Many parents understandably prefer sippy cups with valves that close off any flow opening in the spout until suction is supplied by the child, instead of permanently open holes or slots. The design of such valves traditionally entails a trade-off between flow rate during drinking and leak rate when not in use. Also, many such valves can be difficult to properly clean. Some valves are removable and can be misplaced. Some sippy cup valves are in the form of a flexible membrane with a normally closed slit which opens sufficiently under pressure to enable acceptable flow.